Applied Fourier Analysis : From Signal Processing to Medical Imaging / by Tim Olson.

Format:

Book

Author/Creator:

Olson, Tim., Author.

Language:

English

Subjects (All):

Fourier analysis.

Signal processing.

Image processing.

Speech processing systems.

Differential equations, Partial.

Applied mathematics.

Engineering mathematics.

Fourier Analysis.

Signal, Image and Speech Processing.

Partial Differential Equations.

Applications of Mathematics.

Local Subjects:

Fourier Analysis.

Signal, Image and Speech Processing.

Partial Differential Equations.

Applications of Mathematics.

Physical Description:

1 online resource (XVI, 302 p. 126 illus., 118 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

New York, NY : Springer New York : Imprint: Birkhäuser, 2017.

Summary:

The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects. The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.

Contents:

Introduction: From Linear Algebra to Linear Analysis

Basic Fourier Series

The Discrete Fourier Transform

The Fourier Transform

Sampling and Interpolation

Digital Communications

Radar Processing

Image Processing

Medical Imaging

Partial Differential Equations.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4939-7393-2

OCLC:

1066196379